After a standout season with the Ajax Axemen in 2002–03, Elliott was drafted in the ninth round, 291st overall, in the 2003 NHL Entry Draft by the Ottawa Senators. The second-last player selected in the draft, Elliott was not expected to progress to the NHL. After being drafted, he would spend four seasons with the University of Wisconsin–Madison, serving as a backup for his first two seasons before securing the starting goaltender position in the 2005–06 season. For his efforts, he was selected as a finalist for the 2005–06 Hobey Baker Memorial Award,[1] collecting eight shutouts in 33 appearances, and leading the Badgers to the 2006 NCAA National Championship. He was then signed by the American Hockey League (AHL)'s Binghamton Senators – an affiliate of the Ottawa Senators – on March 23, 2007, and played in eight games with Binghamton near the end of the 2006–07 season.

Elliott in goal during his tenure with Ottawa.

Elliott was invited to the Ottawa Senators' 2007–08 training camp, but was ultimately assigned to Binghamton on September 25, 2007. He was recalled to Ottawa four days later to back up Martin Gerber, as starting goaltender Ray Emery was recovering from wrist surgery. On October 10, Elliott played in his first NHL game and earned the win against the Atlanta Thrashers. Upon Emery's return, Elliott was sent back to Binghamton, where he played in 44 games that season.

On January 9, 2009, Elliott was recalled by Ottawa after being named the AHL's Goalie of the Month for December.[2] He had been a standout in Binghamton, posting an 18–8–1 record with a 2.31 goals against average (GAA) and .926 save percentage. His play earned him the starting position for the Canadian team in the 2009AHL All-Star Game.

Elliott made an immediate impact in Ottawa. The team had struggled all season, with inconsistent goaltending being an issue. Craig Hartsburg, Ottawa's head coach at the time, said of the move, "We need some saves, some big saves, and he's done it down there [in Binghamton]."[3] Elliott would finish the season in Ottawa, sharing goaltending duties with veteran Alex Auld. Elliott's emergence effectively made Martin Gerber expendable to the team, and he would later be claimed on waivers by the Toronto Maple Leafs.

Elliott was nominated for the NHL's Rookie of the Month award for March 2009, though he would lose out to St. Louis Blues forward T. J. Oshie.[4] In January 2010, he was awarded the NHL's First Star of the Week for January 18–24, and named the League's Second Star of the Week for January 25–31.

Elliott signed a one-year contract worth $600,000 with the St. Louis Blues on July 1, 2011.[7] Forming a formidable goaltending tandem with Jaroslav Halák, Elliott revitalized his career, posting a 23–10–4 record while sporting a 1.56 GAA. He was also chosen to participate in the 2012 NHL All-Star Game in Ottawa.

On January 18, 2012, Elliott signed a two-year contract extension with the Blues. The deal carried an average annual value of $1.8 million. Elliott will reportedly earn $1.7 million in 2012–13 and $1.9 million in 2013–14. After taking over for the injured Halák during the first round of the 2012 Stanley Cup playoffs, Elliott led the Blues to a series victory over the San Jose Sharks before ultimately being swept in round two by the eventual Stanley Cup champions, the Los Angeles Kings.

On March 12, 2015, Elliott tied Jaroslav Halák for the Blues' franchise record in shutouts.[10] Five days later, on March 17, Elliott surpassed Halák for the Blues' shutout franchise record.

A 23–8–6 record during the 2015–16 NHL season earned Elliott the starting role for the Blues for the 2016 Stanley Cup playoffs. He led the Blues to a first round victory over the defending Stanley Cup champion Chicago Blackhawks. He made 31 saves in the deciding Game 7 victory on April 25. Elliott and the Blues would then move on to face the Dallas Stars, who had been the Western Conference's number one overall team. Again, the Blues prevailed in seven games. Elliott's only faltering occurred in Game 6 of the series, when he was pulled in favour of Jake Allen after allowing three goals on seven shots. He would rebound the next game, making 31 saves in a decisive 6–1 victory that propelled St. Louis to the Western Conference Finals for the first time since 2001.[11]

During the 2016 NHL Entry Draft, Elliott was traded by the Blues to the Calgary Flames in exchange for a 2016 second-round pick (Jordan Kyrou) and a 2018 conditional third-round pick on June 24, 2016. On October 24, 2016, he won his first game as a Flame against Chicago in a shootout.[12] However, he struggled with the team early, prompting them to switch to Chad Johnson as the team's regular starter. Elliott regained the starting job after starting the season off 3–9–1 with a 3.31 GAA and a save percentage of .885. On June 17, 2017, GM Brad Treliving informed Brian Elliott that he will not be returning to the team for the 2017–18 season.

While attending Newmarket High School, he took the school's boys hockey team to the championship, winning it in 2000. He also attended Newmarket High School with former Blues teammate B. J. Crombeen.

Elliott's father, Bill, is a television director who has worked on numerous Canadian television programs, including The Red Green Show.[17] He resides in Wisconsin during the off-season. Elliott has one brother named Dan.

Elliott was taught the art of moose calling by the late Owen Scott, a champion moose caller. He paid tribute to Scott with a moose painted on the back of his goaltender mask. Elliott also had Casey Jones from Teenage Mutant Ninja Turtles painted on his mask.[18][19] Due to this, his nickname on the Philadelphia Flyers is "moose."[18][20]

During the 2015–16 NHL season, Elliott began wearing all blue pads as a tribute to former Blues goaltender Curtis Joseph, and also had his mask painted with the same design that Joseph wore.[21]